Problem 43 - Elementary Algebra

Question

Fill in the blank with \(<,=,\) or \(\geqslant\). 10 _____ -10

Step-by-Step Solution

Answer

10 > -10

Step 1: Identify the Numbers

The exercise involves comparing two numbers: 10 and -10. We need to determine which of these is larger, smaller, or if they are equal.

Step 2: Understand the Position on the Number Line

On a number line, the number 10 is located to the right of the number -10. In terms of placement, numbers to the right on the number line are greater than those on the left.

Step 3: Apply the Comparison

Since 10 is to the right of -10 on the number line, we know that 10 is greater than -10.

Step 4: Fill in the Blank

Using the result from the comparison, fill in the blank with the correct symbol. Since 10 is greater than -10, we put the 'greater than' symbol (>) between them.

Key Concepts

number line

The number line is a visual representation of numbers laid out on a straight line. It is a fundamental concept in mathematics that helps us understand and compare numbers easily. On a number line, numbers increase in value as they move from left to right. Negative numbers are found to the left of zero, while positive numbers are on the right. This linear arrangement makes it straightforward to determine which numbers are larger or smaller.

Using a number line, you can visually compare two numbers and see their positions relative to each other. For example:

• A higher number is positioned further to the right.
• A lower number is positioned further to the left.
• If two numbers are the same, they share the same point on the line.

This concept is crucial for comprehending inequalities and helps immensely in solving comparison problems. By observing the placement of numbers like 10 and -10 on a number line, you can easily see that 10 is to the right of -10, confirming that 10 is greater than -10.

comparison of numbers

Comparing numbers is a basic arithmetic operation that determines the relationship between two numbers. This comparison can tell us whether a number is greater than, less than, or equal to another number. The number line is often used as a tool to facilitate these comparisons.

When comparing numbers, consider the following:

• A number further to the right on the number line is greater than a number to the left.
• A number further to the left is less than a number to the right.
• If two numbers align on the number line, they are equal.

In the exercise example, we compare 10 and -10. By locating these on a number line, we see that 10 is indeed to the right of -10, making it larger. Thus, we confidently state that 10 is greater than -10.

algebraic symbols

Algebraic symbols like <, =, and > are crucial for expressing mathematical relationships and comparisons succinctly. These symbols serve as a universal language to convey whether one number is less than, equal to, or greater than another.

Here's a quick guide on understanding these symbols:

• < : This symbol means 'less than' and is used when a number on the left is smaller than a number on the right.
• = : This symbol signifies 'equal to' and implies both sides have the same value.
• > : This symbol means 'greater than' and is used when the number on the left is larger than the number on the right.

In our exercise, since 10 is on the right of -10 on the number line, we use the 'greater than' symbol, resulting in the expression 10 > -10. Understanding these symbols allows us to clearly and efficiently describe the relationship between numbers in algebraic expressions.